Problem: Solve for $x$ : $2x^2 - 2x - 4 = 0$
Dividing both sides by $2$ gives: $ x^2 {-1}x {-2} = 0 $ The coefficient on the $x$ term is $-1$ and the constant term is $-2$ , so we need to find two numbers that add up to $-1$ and multiply to $-2$ The two numbers $-2$ and $1$ satisfy both conditions: $ {-2} + {1} = {-1} $ $ {-2} \times {1} = {-2} $ $(x {-2}) (x + {1}) = 0$ Since the following equation is true we know that one or both quantities must equal zero. $(x -2) (x + 1) = 0$ $x - 2 = 0$ or $x + 1 = 0$ Thus, $x = 2$ and $x = -1$ are the solutions.